Calculating means



Nov. 3, 1959 N. L. M. RoUcHE. 2,911,149

CALCULATING MEANS Filed Aug. 8. 1956 I f 5 Sheets-Sheet 1 A Harney Nov. 3, 1959 N. 1.. M. RoUcHE 2,911,149

CALCULATING MEANS Filed Aug. 8, 1956 5"Sheets-Sheet 2 Inventor N. LMROUCH Www/4 1 Attorney f Nov. 3, 1959 N. L. M. ROUCHE CALCULATING MEANS 5 Sheets-Sheet 5 Filed Aug. 8, 1956 Inventor N. L. M. ROUCHE Nov. 3, 1959 N. L.. M. RoucHE CALCULATING MEANS Fied Aug. 8. 195e 5 Sheets-Sheet' 4 E mw m nO IM L. NDV E .4. 4/ VE 9 0 cw M 6 Nov. 3, 1959 N. L. M. RoucHE 2,911,149

CALCULATING MEANS 'Filed Aug. 8, 1956 v 5 Shets-Sheet 5 .rect value is found, this 'indicates United States Patent() i cALcULA/TING MEANS Application August 8, 1956, Serial No. 602,857

Claims priority, application YNetherlandsv n.September 17, 1955 7 Claims. (Cl. 23S-'153) The invention relates to calculating means and more Vparticularly to means for 'calculating' aV digital function which can take any value out of p different digital values from to p-l, where pis a predetermined integer.

Such calculations are required, for example in the case of numbers, the digits fof which satisfy the same predetermined function for any number. numbers have, for instance, tov be keyed by an operator, as the digits of the number are keyed, this predetermined function is calculated and if another value than the corthatthe operator has made a mistake.-

' Thefollowing type of function is particularly'useful in order to determine in all cases if a `-single digitalerror has been made or if a single transposition' of twodigits v has occurred =nl y Z'kiai mod.. p i=1 Y a'lfaz, an represent the n digits of the number, a1

being theY digit of highest rank, k1, k2, kn represent coefficients which may be independent of the value of the digits but which depend on the rank. It is clear that such a function can only have p diiferent values since the least non-negative residues with respect top are always taken. Hence, one 'should'be lsolely concerned with integers from 0 to p-l 4since any other integer of higher value will in fact be treated Vas one of this group *of p digits since lthe least non-negativeV residuefwith respect to p will be taken. j

Suitable lvalues for the coefficients kiand for p have already been discussed in application o f Linsman, Serialy No. 484,7I5, iiledTanuaryZS, 11955'.y YTo summarize, if any vsingle digital/error is to be detected, the product of any coecient by 'any'` number from* 1` to p-l should be different from 0 when taking the least Then, wheny these 2,911,149 -Patented Nov. 3, 19,5 9

ICC

Z numbers. This means that the numbers are really on the scale of 1l but if the decimal notation is to be retained one can simply omit those numbers which would include the digit 10. v

An` arrangement has alreadybeen described in said abovek mentioned application to compute a function of the type given by (l). l y An object of the invention is to generalize the arrangement previously disclosed. i'

In accordance with Va iirst characteristic of the invention, calculating means to calculate a digital function which can take any value out of p ditferent digital values from 0 topf-#1,? where p is a predetermined integer, are characterised by the inclusion of` a'rst and a Ysecond counter each with at least p stable and distinct conditions and each able to be stepped cyclically from one condition to the next, p steps causing the return of the counter to its initial condition, and-,by the fact that starting with the first counter in a iirst initial condition and with the second. counter in a second initial condition,said first counter is stepped at one rate while simultaneously said second counter is steppedy at r Vtimes said rate, r being an integer, means being provided simultaneously to stop this stepping action for both counters when said first counter reaches a iirst predetermined condition, and that with said first counter in said rst predetermined condition and with said second counter in the condition attained, said second counterV is then stepped at one rate non-negative residue'with respectjto p, p (p'p) being diiferent ranks is to-be -detected, the product of the dify ference between any two coeicients by any number from ly to p-1 shouldy also .be diiferent from 0 when taking the f least non-negative residue'with-l respect to p. For decimal numbers a convenient scheme is to use p=ll, since the second Vabove condition can then be satisfied for ten c0nsecutive ranks as oney can assignV the coefficients 1 vto 10 in any suitable order to these ranks, While the tirst above condition is always satisfied. For other bases, other values for p might be chosen but it should be remarked that once a value of p has been chosen. which is suitable to satisfy the above two relations and which is therefore higher than or equal to theA base, the latter doesnot play a particular part in the computation of the function of the general type mentioned above. When using p=l1 for decimal numbersforsome values of n-l digits of an n-digit number, it will be found that the nth digit has to be equal to` 10 to result. in the function of the type mentioned above giving the predetermined value for allv the times said rate, s being an integer, means being provided simultaneously to stop the Istepping action for both .counters Vwhen said second counter reaches a second predetermined condition, whereby the condition finally attained by said first counter is a digital function of the initial :conditions of the rst and the second counters and deiined by Y (2') where x1 is the number of steps required to bring. the first counter from `said iirst initial condition to said` rst predetermined condition, y, is the number of steps required to bring the second counter from said second initial condition to 'said vsecond predetermined condition, and xm is the number of steps required to bring the iirst counter from the condition nally attained to said iirst predetermined condition.

If the Relation 2 above is used n times, starting with "the initial conditions x1 for the first counter and y1 for the second counter, and each time placing the second counter ina new condition, such as y2, ys, yn, the iinal condition x 1 of the iirst counter will be given by This relation'should be assumed to be valid when taking kthe least non-negative residues with respect to p but in order to simplify the notation, mod. p is no longer .used in this'. or further relations, but the sign E will be retained.

Eachcondition of the second counter y1, y2 yh can correspond to a digit of a number, ite. the conditions and the digits form isomorphic groups. Various functions are suitable provided they uniquely deiine the digits. For example, the cube of each decimal digit from 0 to 9 could be used since this produces l0 dilferent digits with a unique correspondencewith the original digits when taking the least non-negative residues with respect to l1. On the other hand the square of the digits would not be a suitable function with 1-1 as modulus, since such a unique correspondencel would not then be produced.

Similarly, the iirst and the last conditions, x1 and xm.; of

the first counter could also be similar functions of the digits.

Moreover, the correspondence between the digits and the conditions of the rst counter need not necessarily be exactly the same as that between the digitsand the conditions of the second counter. This was already the case -in the embodiment disclosed in the application mentioned above. In general, one can use a first -linear rela- ;tionship between the digits and the conditions of the first counter and a second linear relationship `between the digits and the conditions of the second counter, i.e.

where-b1 and b 1 are the digits respectively-correspond- 'ing with the conditions x1 and xml ofthe rst counter `and where ai is the digit corresponding to yi on the second counter. The parameters uo, u1, v and v1, defining the two' linear relationships are predetermined integers between'O and p-l for uo and v0 and between 1 and p-1 for u1 'and v1.

Relation 3 can then be transformed by using Relations Y (TSW-1 There are three terms in the right-hand part of the.r relation and only the third is a function ofthe various digits'V of the number. It will be recognized that thisv func- 'tion is of the general type given by (l). Hence, with the various parameters all predetermined, if the digits of any number satisfy the Relation '7, one can ensure that with a single digital error or with a single vtransposition of two digits, Relation 7 shall not be satisfied and the error can be detected. Of course, any other type of error has only one chance-out of p of being unnoticed. It is clear that the parameters uo, v0, b1 and b+1 merely complicate the Relation 7. The only possible advantageV of not having these four parameters equal to 0 appears to render the function more complicated and vhence more diflicult to reproduce by some unauthorized `party. When these fourparameters` are equal to 0,'-Relation 7 simply be# comes Y =n E (t8) "af 0 (8) i=1 It will be observed that the effective coeicients which multiply each digit and which are functions vof the ranks occupied by the digits form a cyclic group, i.e. a group iwhose elements can all be expressed asA powers of a single element. The law of formation for this group is multiplication followed by reduction to the least positive residues with regard to p. The order of this group, i.e. the number `of its elements, can evidently not be higher than p-l and if a group of order p-l can be obtained, this means that transpositions of any two digits occupy'- ing any two ranks out of p-l consecutive ranks can alwaysbedetected with absolute certainty. With p=ll, rs=1 will merely give a group of order l comprising onlyunity. In that case all the coefficients are equal, transpositions cannot be detected and only digital errors can be traced. With rs= l0, a group ofeorder 2 comprising l and 10 can be obtained. In this'case, transpositions of adjacent digits canV always be detected. With rs=3, 4, 5 or 9, a group of order 5 comprising the elements 1, 3, 4, v5 and -9 is generated'. The order of the coeicients will depend on the generating element, e.g. l, 3," 9, 5, 4 when 3 is the generating element, but in all casestransi 4 positions between any two digits occupying ranks not separated by more than three intermediate ranks can always be detected. For practical purposes this may be considered as quite satisfactory, but it is to be remarked that with rs=2, 6, 7 or 8 itis then possible to generate a complete group of order 10. lIn that case, transpositions of two digits whose ranks are not separated by more than eight intermediate ranks Will always be detected; v

Hence, Afor p=1l; rs=2 is among the preferred values and this can .be obtained either with r=1 and .9:2, as in the above mentioned application, `or with r=2 and S=1.

Another object of the invention is to reduce the maximum time of calculation required for each digit of a number which is to be verified against digital errors or transpositions.

In accordance with another characteristic of the invention, calculating means to calculate a digital function which can take any value out of p diierent digital values lfromO to pf-l, where p is a digital integer, are characterised by the inclusion of a iirst and a second counter, each ,with at least p stable and distinct conditions and each able to be stepped cyclically from one condition to the next, p steps causing the return of the counter to its initial condition. Starting with the rst counter in a rst initial vcondition a signal is applied to both counters under the control of a bistable device which is in such condition that said signal is only efrective with respectto the second counter `to place the latter in a second initial condition. The first counter is then stepped at one-rate, while simultaneously said second counter is stepped atvr times said rate, r being an integer, means being providedto simultaneously stop this steppingy action for both counters when said rst counter reaches a rst predetermined condition, as well as to place said bistable device into its second condition. A signal is applied to both counters under the control of said bistable device in its second condition but is `only effective to place said li-rst counter in a third initial condition, said second counter remaining in the condition attained. Said second counter is then stepped atone rate while simultaneously `said lirst countcris stepped at s times said rate, s being an integer, .means being provided simultaneously to stop the stepping action for bothk counters when said second counter reaches A a second predetermined condition as well as 'to place said bistable device into its iirstcondition. Thus, after each stepping action, the Vconditionattained by the counter, stepped at 'r or .s times the rate at which the 4other counteris simultaneously stepped, is a digitali-unctionV ofthe initial conditions of both counters before said stepping action and is delined by v-rst counter from said first initial condition to said first predetermined condition, y2z 1` is the number of steps required to bring the second counter from said second -initial condition to said second predetermined condition, y2; is 'the number of steps required to bring the second counter to said second predetermined condition from the condition attained after having been stepped at r times the rateof the rst counter, x2, is Ythe number of steps required to bring the iirst counter from said third initial condition to said first predetermined condition, and x2+1 is the'number of steps required to bring the rst counter to said rst ,predetermined condition from the condition ,attained after'having been stepped at s times the rate of the second counter.v

The repeated use of the Relations 9 and l0 gives the condition x2+1 of the rst counter after 2n alternate operations, i.e.1the second counter is first placed into condition" y1), the first. counter is then placed in condition x2,

`should be used instead of Relation 11.

the second counter is then placed; in condition ya, the iirst counter is then placedin condition x4,etc. The 1e v' latioin which is of asimilar type as that given by v(3,-) 1s After yet another condition y2n+1 is impressed on the second counter, the new condition of the latter becomes ym, given by Y -Here again, there can existlinearrelationships between the conditions :of the .counters `and the digits of the num- .;ber. llt b1 and b2+1 are the digits respectively corresponding with the initial condition x1 and thellast con- .dition x2 1 respectively (on the-iirst counter), the Rela- ,tion 4 applies Ias well as Also, since the digits of even rank, starting with the highest rank are applied to the first counter and since the-digits of odd ranks are applied to the second counter,

Here again, only the third vterm of the right-hand expression is a `function of the various digits al, a2, vc12 1, 112 of a 2n digit number.

Hence the parameters uo, v0, b1 and b2n+1 serve only to complicate the function to be satised by the digits, and one may as well have `these four parameters all equal to 0. In that case, Relation 16 becomes Y This relation is seen to be similar to (8) but as each digit is stored on one or the other counter, it is only necessaryv'to step both counters untilvthat on which the digit was not stored reaches its predetermined or 0 condition. Hence, the maximum time of computation isrhalved.

Relation 17 is valid after 2n such operations,` i.e. the number comprises an even number of digits. After 21H1 operations, thus for an odd number of digits Relation 12 Using (.12) in conjunction with (11) as well as (4), (14), (15k) and Mue-evo)` (re) 1 which is thus the equivalent of (16) in the case of an odd number of digits, i.e. 2n|1. If the four parameters uo,

y0, b1 and b2n+`2 are all made equal to 0, (19) becomes Considering 17) and (20) it is Vseen that the coeffi- .cients which .effectively multipli/the digits of even rank .starting with .the highest rank, form a cyclic 4group generated by rs. If rs is chosen so that a group of vrp--"1 different coeicients is produced, the coeicients for the digits of odd rank will necessarily be contained in this group. As the digits of odd ranks are intermeshed with the digits of even rank, one will in general lnot be able to detect in allfcases a transposition of two digits which are not separated by;more than p-3 ranks, this being the most eiicient arrangement. However, ifrs is chosen vso as to generate a group of smaller order than p-1,it will be possible to select suitable values for r, s, v1, and u1 so that the coefficients of the digits of odd rank are dilerent from those of even rank.'V

vThe following example is useful to explainlthisppoint. Considering (17) and assuming ,that .p :is equal 'to 1:1 whereasr rs is equal to 4, the coecients of the digits of even rank will be f l being the coefficient. of the digit a2n. These coeticients form a cyclic subgroup of order 5 out of the cyclic group ofr'order l() comprising :all the numbers from vthe full group of coecients becomes where the underlined coecients'are those of the digits of even rank, l being the coecient Vof aan, while the other coeicients are those of the digits of'odd rank, 6 being that of a2 1. vIn the particular case where would be chosen vas equal to 2, the above series of coeilii cients would become.:

(still with rsEland il 6) Only in the case of series such as the one given by (24) for an even number of digits, will the same lseries be applicable for an odd number of digits. f From 17) and V(20) it is clear that the particular condition is a particular solution of which isl l It is of course not absolutely essential that the coefcients should always be different for `any set of p-I consecutive ranks, since transpositions between digits of widely separated ranks are unlikely to occur, but as this can in general be obtained without any increase in the equipment which is about to be described, one might as well select the values of the parameters in order to btain the maximum safety against transpositions of digits.

The above-mentioned and other features and objects of this invention and the manner of attaining them will become more apparent and the-invention itself' -will be best understood by reference to the following description of an embodiment of the invention taken in conjunction with the accompanying drawings, in which:

Fig. 1 is a diagram representing a first embodiment of the invention using two counters;

Fig. 2 is a diagram showing the details of a control circuit shown as a block schematic in Fig. l;

Fig. 3 is a diagram of wave forms of pulses used to operate the circuits of the various gures;

Fig. 4 is a diagram showing details of a particular circuit shown in Fig. 2 and designed to suppress undesirable elects of mechanical contact vibrations; Y

Fig. 5 is a diagram representing a second embodiment of theinvention;

j', Figpis a diagram showing details of modications to be brought tothe circuit of Fig. 2 in order to iulil the requirements of the circuits of Fig. 5;

"Fig. 7 is a diagram representing a third embodiment of the invention; n

Fig. 8 is a diagram showing details of further modica- .tions to be brought to the circuits of Figs. 2 and 6 in order to ull the requirements of the circuit of Fig. 7.

Using the coe'icients given in (24) above, a set of numbers can be determined in which the units digit is the proof digit, the tens, hundreds, etc. digits representing the actual number. Thus, the number 25 would have a proof digit at the end'which would be 4, making lthe number to be keyed up 254. It will be seen that (1X4)l-(2 5)l(4 2) when divided by l1 will give a remainder of 0. The number 26 would have 2 as a proof digit. 'I'he proof digit for number 15 would be 8. Whenever the proof digit iigures out to be 10, that number-is not used, so as to avoid complicating the circuits. Thus 6, 14, 22, 30, 49I etc. are excluded from the numbers used.

In the electronic circuit to be described, a number including the proof digit is keyed up and the circuit will produce a ysignal if keyed correctly. If digits are transposed, as explained, the signal will not be produced. v

A irstembodiment of the invention will be tirst described in relation to Figs. 1, 2, and 3. v

Fig. I'shows the two counters CTI and CTZ both with eleven distinct electrical conditions. These counters are of the pattern shift register type and may for instance be realized in accordance with the US. patent to Odell, No. 2,649,502, issued August 18, 1953, Where each stage comprises a cold cathode tube plus associated elements. In brief, such a counter operates in the following way. The cathodes of all the tubes are commoned together and the common cathode lead can be used to provide positive driving pulses each of which will cause the advancement of any pattern registered on the counter by a single step. The positive rise of the pulse causes the extinction of all the cold cathode tubes which are ionized and a pulse is created in each of the corresponding anode circuits. Such a positive pulse in the anode circuit of a tube is applied to the starter electrode of the next tube but will only become effective to strike this next tube,

when the positive driving pulse at'the commoned cathodes has disappeared. Y

Each counter such as CTI is represented by a rectangle divided into eleven squares each indicating a possible stable condition or stage of the counter. In addition to the two counters CTI and CTZ, Fig. I shows four gates G1 to G4, which are represented kby circles with input leads terminated by an arrow and pointing towards the centre of the circle and with an output lead also in line with the centre of the circle. v The numeral inside the circle indicates the number f-inputs which must be simultaneously energised to provide an output. The four gates shown are basic'. coincidence circuits or And gates. Fig'. 1 also shows a control and startingv circuit CSC as a block diagraml which is detailed in Fig. 2.. This will be used to control the two counters CT 1 and CTZ.

The operation following the depression of a digit key, consists in adding the value ofthe new digit to twice the value already stored in counter CTI, the result being expressed as the least non-negative residue with respect to 1l. If it is assumed that CT 1 is in condition 2, and that CTZ is put in the condition indicated by 8 as a result of the key corresponding to 8 being depressed, pulses will simultaneously be applied to' CTI and CTZ to drive them, but for each pair of stepping pulses applied to CTZ, only a single stepping pulse will be applied to CTI. Therefore, after two pulses have been applied to CTI, this counter will now bein the 0 condition while CTZ will be in the first condition since CTZ, as well in factas CTI, is operated in ring counter fashion in order to obtain the least non-negative residues with respect to 11. The arrival of CTI in its 0 condition will be detected and as a result, both CTI and CTZ will now be driven in syn` chronism, i.e. for each pulse applied to a counter a pulse is also applied to the other counter. Therefore, when .CTZ reaches its 0 conditionfCTI will now be in its first condition. The arrival of CTZ in its O condition can also be detected and the basic operation resulting from the depression of the digit key corresponding to 8 is now ended. Counter CTI is now in its rst condition instead of being originally in its second condition and this is the desired operation since {2(2){8} mod. l1 1.

The control and starting circuit CSC represented in detail in Fig. 2, includes a number of relays, and a number of gates symbolically represented as already explained. Those gates with a l inside the circle are merely mixers, or buiers, or Or gates, while the gates with a2 or 3 inside the circle are coincidence gates necessitating the simultaneous energisation of two or three inputs to deliver an output signal. In addition to the gates, bistable and monostable circuits are represented by rectangles divided vinto two squares. Input signals are shown asarriving on the long sides of the rectangle, while the output signals depart from the short sides of the rectangle. For the bistable circuits, one square is labelled 0 while the other square is labelled l. It is assiuned that an input signal to the square 0 will drive the bistable circuit to the 0 state (or leave it in that state) whereby an energising condition is provided at the output of the O-square. A similar condition applies to the l-square. Preferably, the 0 condition corresponds to the initial or normal condition eventually obtained after reset, as will be later explained. For the monostable circuits, O is the normal stable condition while the other square has been provided with an indication showing the time constant of the circuit, -i.e. the time after which the circuit returns to the 0 condition after having been driven to its unstable kcondition by an input signal.

No particular reference will be made to the sign and shape of the pulses, nor to their amplitudes, except when necessary to obtain a clear understanding of the operation. A distinction is however made so :far as necessary between steady and transient conditions. 'For transient conditions, the output lead is interrupted byv a condenser sign to indicate that the signal isndiierentiated For example, when the monostable circuit MSD is driven to its unstable condition, a steady signal on the output lead monostable circuit MS1 is driven to its unstable condition, for a period of 15 microseconds, a signal will only appear on the output lead when the monostable circuit returns to its stable condition, i.e. a short trigger pulse will 'be delivered 15 microseconds after the input pulse. Dilierentiated output signals should be assumed to be active for one polarity only, but no indication of this polarity is believed to be necessary for a symbolic representation, such as the one shown, since all monostable circuits using differentiated output signals are essentially delay circuits, i.e. the active diiferentiated output signal is that produced when the monostable circuit returns to its stable condition. In any case where there might be ambiguity, ia special explanation will he given to deiine the active signal.

The circuits will now be described in relation to a particular example of an operator being required successively to key information appearing on cheques. For each cheque, iirst the account number should be keyed and then the amount. The proof circuit should be operative for the yaccount number but it should not be operative for the lamount since the amount will be assumed to be ordinary numbers whose digits do not lnecessarily satisfy the relation previously mentioned. The account numbers will be keyed while the typewriter carriage is on the left. Thereafter, a keyy will be depressed which will cause printing of the keyed iigures and the'displacement of the carriage to the right-hand position in which the yamountcan now be keyed. A shift to the right will take place only if the laccount: number is proved to be correct. If not, printing will not take place in response to the operation of the key after typing the account number, the carriage will remain in the lefthand position and a signal will be given to the operator indicating that an error hasv been made. Upon Ibeing notified in this manner, the operator can only depress a cancel key which will erase the mechanically or electrically stored account number which was ready for printing, and which will also restore the proof circuit to the normal condition ready for making a new proof as the account number is rekeyed. After keying the amount, the carriage will be returned to the left, in readiness for keying the account number of the next cheque,

The storing and printing of the two types of numbers is however no part of the invention, and those details given above have been mentioned merely to explain briey how the circuits shown can be fitted to a business machine of the type considered. When power is first applied to the circuits of Figs. 1 and 2 it is clear that some of the electronic circuits might be in an initial arbitrary condition. This would be they case for the bistable circuits such as BVS0 in Fig. Zand for the counters such as CT1 in Fig. l where an entirelyarbitrary pattern of cold cathode tubes might initially be ionized. One of the tasks of the circuits CSC detailed lin Fig. 2 is to place the circuits in their proper conditions so that operations can be started.

Vsimultaneously through make contact [r1 for Lar and through make contact [r3 and break contact lbrl for Cr. The operation of Lar causes the energisation of Lbr through make contact larl. The operation of relay Cr causes thesimultaneous energisation of relays Car and Cbr, the first throughlmake contact cr1` and the second through make contact crz. Relay Cbr locks independently of CrV through its make contact cbrl in series'with the Vwinding of Ccr and break contact cdrl. As a result of the operation of relay Lbr, Cr releases followed bythe release of Car and the operation of Ccr which is no longer shortcircuited by contact cr2 and which is now energised in series with Cbr, As a consequence of the operation of relay Ccr, Cdr energises causing the release of Cbr and Ccr which last release produces the de-energisation of Cdr. At this moment the sequence is completed and only relays Lr, Lar and Lbr remain operated, relays Cr, Car, Cbr,

magnetic relays, various operations have taken place in the electronic circuitry which operations occur at a much more rapid rate than those performed by the ordinary telephone type relays mentioned above.

Upon relay Lr being energised, contact [r2 is opened and the potential at terminal P6 Which was applied through this contact to the bistable circuit BSO is suppressed. This results` in BSO being placed in its one condition. This may for example take place in practice by causing the grid of one of the tubes forming a fliplop to have its potential increased due to the opening of contact [r2 increasing the resistance between this grid and ground, this grid being on the other hand connected to the Vll.T. supply through the anode of the other tube forming the nip-flop and this in conventional manner. If the not already conductive, its plate cathode space will now -b'eV ionized while the other tube will become non-con- -Iductive.

the connection to terminal P6 through make contact larg but this will not have further effects.

The operation of relay Lm' Will re-establish ving the connection between terminal P5 and the circuit MP. This opening does not however affect the state of this last circuit. When relay Car operates, the connection will be reclosed through make contact carl and this will create a pulse which is eiective to pass through the circuit MP so as to trigger the monostable circuit MSO which is connected to the output of MP, into its unstable condition and this for a period of some 300 microseconds.

The bistable circuit BSO-being in its 1 condition and the monostable circuit M50 being in its unstable condition, the gate G5 is now ready to pass the first Pa pulse which will appear at the corresponding terminal.

The Pa pulses together with the Pb'and Pc pulses are represented in Fig. 3. All three types of pulses have the same period of 200 microseconds but whereas the Pa and the Pc pulseslare trigger pips, the Pb pulses have a dura- Vtion of some 30 microseconds. The VPb pulses have their Yleading edges dephased by a half period, i.e. microseconds, from the Pa pips. The Pc' pips lag behind the Papips by some` microseconds.

than ythe period of 200 microseconds separating any Pa pip from the next so that at least one Pa pip, and at most two, will be able to pass through the gate G5 While MSO is in its unstable condition, PSO being in its 1 condition.

The single or first Pa pip passing through G5 will trigger the bistable circuit BSI into its l condition in the case that it was not initially-in that condition. The Pb pulse immediately following the starting Pa pip, after 100 microseconds will then be able to pass through the gate G7 and will be applied in parallel to the gates GS and G10. This Pb pulse may be allowed either through G8, or through G10 or it will not be allowed to go through at all, this depending on the initial condition of the bistable ycircuits BSZ and BSS. Considering gate G8 only, if the rst Pb pulse is not able to go through that gate, it means that BS2 is initially in the 0 condition.

However, the irstPc pip'which follows the rst Pb pulse,

60 microseconds after its leading edge, will be able to pass through gate G6 and trigger the bistable circuit BSZ which operates as a scale-of-two counter with a common input. Hence, if BSZ was initially in the condition it will now pass to the l condition, whereby the second Pb pulse will be able to pass through G8 and reach terminal P10 as well as terminal P9, the latter through the mixer G9. respect to the state of conductivity of the gate G10, for

`every pair of Pb pulses, one will be able to reach terminals P10 and P9. By referring to Fig. l, it is seen that the initial arbitrary patterns on the counters CTI and CTZ will therefore both be advanced by one step for every pair of Pb pulses passing through gate G7. It should be noted that at this moment relay Cr is still operated as relay Lbr will take a sufficient time to operate so as to permit the electronic operations presently described. Consequently, contacts cr., and cr are open andas the patterns on CTI and CTZ are advanced, they do not merely circulate but progressively disappear.

If BSS `is initially in its l condition, this means that those Pb pulses which are not allowed through G8 will be allowed through G10 and accordingly more pulses will appear at terminal P9 which means that the pattern on counter CTZ will disappear more rapidly than the one on counter CTI. This is however of no consequence whatever since the time during which this process takes place will be sufcient to permit an adequate number of Pb pulses to be applied to each counter to wipe out the original patterns, and this irrespective of the initial conditions of BSZ land BSS.

The wiping out process for both counters will thus continue until relay Cer is energised following the release of relay Cr. The time interval between the operation of relay Car and the release of relay Cr should be such as to permit somewhat more than 22 Pb pulses to flow through the gate G7, and this while recirculation is prevented for both counters CTI and CTZ. A period of about 6 milliseconds or more would therefore be satisfactory. When relay Ccr energises, contact ccr2 is opened and a signal reaches the Zero input of BSI through the mixer G11 since terminal P6 is now disconnected from this input. This will have the same effect as the one described for the l input of BSO (opening of contact lf2) and BSI will now be placed in its 0 condition, the Pb pulses being no longer able to ow through the gate G7. A similar resetting action will take place for the bistable circuits BSZ and BSS which will also be driven to their 0 condition, the last circuit through the mixer G12.

When BSI is driven to its 0 condition, a trigger pulse is produced to drive the monostable circuit MSZ from its stable to its unstable condition in which it will remain for a period of 30 microseconds. This is for a purpose which will appear later but at the present time this operation will be of no consequence, since the trigger pulse generated by MS2 when it returns to its stable condition after 30 microseconds will feed the 1 input of BSS but this will haveno effect since BSS is maintained in its 0 condition due to the opening of contact ccrz, the opening period covering the pulse. Also, the trigger pulse generated by MS2 will drive a further monostable circuit MSS from its stable to its unstable condition and this also for a period of 30 microseconds. MSS will therefore apply a further pulse having the same length as the Pb pulses to the counter CTZ through the mixer G9, but this will be without eifect as this counter is already emptied (no tubes are ionized).

The purpose of the auxiliary circuit MP is to ensure that only a single pulse is applied to the monostable circuit M50 upon kthe closure of contact Carl, or upon the reclosure of one of the ten key contacts such as k12 in series with the parallel combination of carl and cra.

Vibrations of carl when Car operates, of cr3 when yCr releases, assuming that carl would still vibrate, and

Accordingly, whatever happens With 254 will be assumed.

strongest vibrations of the key contact, such as k12, upon the release of the corresponding key, could start undesired operations.

An embodiment of the circuit MP is shown in Fig. 4, and it is seen to include two monostable circuits M84 and MSS with respective time constants of 150 microseconds and 5 milliseconds. When the rst pulse created by the closure of the contact carl is applied to the monostable circuit MSO through the gate G13 which is conductive, since MSS is in its stable condition, M54 will be driven to its unstable condition. When M84 returns to its stable condition, 150 microseconds afterwards, a trigger pulse is generated at its output which will drive MSS into its unstable condition for a period of 5 milliseconds. During these 5 milliseconds, the gate GIS will be blocked and no further pulses can therefore reach M during that time. A period of 5 milliseconds is chosen as an example and should be sufiicient to cover the interval of time during which further closures of carl or of the key contacts such as k12 might occur due to vibrations. A time constant of microseconds has been chosen for MS4 as it is smaller than the time constant of MSG and consequently, the gate GIS will be blocked before MSO has returned to its normal condition from which it could again be triggered due to vibrations.

When contacts cdrg (Fig. l) close as a result of the operation of relay Cdr, a suitable potential at terminal P14 is applied to the 0 stage of counter CTI to ionize the last tube of this counter. This will be the only tube which is conductive in counter CTI, no tubes being conductive in counter CTZ, and the circuits are now ready for the keying of the iirst account number.

To x ideas, the keying of the account number This number is one of those satisfying the condition explained previously since 4(2)-{2(5)}-l(4)0 mod. 1l.

When the iirst digit 2 is keyed, the corresponding key contactkgl will be closed to ionize the tube corresponding to the second stage of CTZ. A second key contact kzz ,will be opened (not actually shown in Fig. Z but included in the series k12 km) without effect. When the key is released, contact km will be the first to open, this being followed by the reclosure of contact k22. As described previously for the closure of contact carl, the closure of contact k22 will be effective to trigger MSO through MP and consequently, the next Pa pip will trigger BSI to its l condition.

VThe iirstf Pb pulse following the triggering of BSI into -its l condition will go through G7 but it will be unable to pass G8 and G10 since on the one hand BSZ is in its 0 condition and since on the other hand BSS is also in its O condition. This last bistable circuit has a double function. Its first function is to distinguish between the arrival of CTI in its 0 condition and the arrival of CTZ in its 0 condition. First it is the arrival of CTI in the 0 condition which is to be detected since this will indicate that the correct result of the operation is now indicated by the position of CTZ. After this, it is however required to return this result on CTI and this will be done when CTZ arrives in its 0 condition. These twov operations must however be distinguished since during the first, CTI is driven at half the rate used for driving CTZ, i.e. r=2, while during the second operation both counters are driven at the same rate, i.e. s=l. A second function of BSS is to authorize the printing of the amount of the cheque if, and only if, the account number has been correctly keyed. This is performed in conjunction with the gate GS (Fig. l) which delivers an output signal whenCTI is in the 0 condition and while simultaneously, BSS is in its l condition. As initially counter CT 1 had to be placed in its 0 condition before keying the account number, BSS is initially put in the 0 condition, sol that it is not possible for the operator -to obtain an O.K. signal permitting her to key the amount -same time BSS is now in its 1 condition.

` CTI is in its .O condition, Ythe addition of twice Oto the Value of the first digit need not be performed and for ,the rst digit only, one will iirst detect the arrival of CTZ in its condition after driving CTI and CTZ at the same rate, an operation which for the digits of lower rank would only be the second operation. l

'The rst Pc pip will triger BSZ to its I condition and accordingly the second Pb pulse will be able to pass through gate G8 and reach terminalsl P9 and P10, the iirst through the mixer G9.A Every even Pb pulse will be able to reach these two terminals while all the odd Pb pulses will be blocked by gate G10. Hence, both counters will be drivenV at the same rate until CTZ reaches its 0 .condition while CTI reaches its 2 condition. The initial conditions of the two counters have thus been interchanged as required and the Pc pip following the Pb Vpulse whose disapearance placed CTZ in its 0 condition, will trigger BSZ to the 0 condition and in so doing will deliver a trigger pulse at terminal P7 which will be able to pass through the Ygate GZ (Fig. 1) and reach terminal P113. This pulse will trigger MSI to its unstable condition and'after l5 microseconds a pulse will be fed to gate G14. Since BSS is in the 0 condition, the pulse will pass through G14 and through the mixer G11, will trigger BSI back to its 0 condition.

From that moment, the flow of Pb pulses through gate G7 is stopped and counter CTI will remain in its 2 condition which it has now attained. Counter `CTZ will not however remain in its 0 condition, since in preparation for the keying of the next digit it is desirable to wipe out Vthat counter altogether. Y

This will be performed due Vtov a trigger pulse being generated vby BSIv upon its return to the 0 condition. 'This triggers the monostable circuit MSZ and 30 microseconds afterwards, when MSZ returns to its stable condition a further 'trigger' pulse is generated to trigger a furthermonostable circuit MSS, from its stable to its unstable condition. The triggering of MSS will create a 30 microsecond pulse which will be applied to terminal P9 through the mixer G9. This will drivelC'TZ by one step, but since gate G4 (Fig. l) is now blocked as BSI has returned to its 0 condition, tube 0 in CTZ will 'be deionized without tiring tube I.' Finally, another consequence of ythe trigger pulse generated by MSZ will be that BSS will now be put in its 1 condition.

'The next digitv 5 will now be keyed resulting in BSI v'being placed in its 1 condition in the same way as previously described. This time however, the first Pb pulse following the Pa pip which put BSI in its l condition,

will be able to pass not only the gate G7 but also the gate G10 since BSZ is in its 0 condition while at the I Y Hence, the 'first Pb lpulse will be applied to 'terminal P9, through the mixer G9, and therefore to, counter CTZ whichfas a result of the keying of the second digit 5` is in its 5 condition.` rThisiirst Pb pulse will therefore cause CTZ to pass to its 6 condition while CTI remains in its 2 condition. Thereafter, the even Pb pulses-will pass through :G8 to reach terminals P9 and P10 in'order to drive both counters, but the odd Pb pulses will continue to drive counter CTZ.

In `this manner it will ,be appreciated that after every even Pb pulse, `CTZ has been driven by twice as many Pb pulses than CTI. VWith modifications to the circuit, the same result could of course `be obtained by applying the odd Pb pulses to both counters while the even Pb pulses would only be applied to counter CTZ. In that case, the operation would be terminated after an even Pb pulse is applied only to counter CTZ. l

After-counter CTI has been driven for the second time,

' it will reach its 0 condition. At that moment, CTZ has been driven four times and has now reached its -9 c ondi tion.

be remarked that gate GS can deliver-'an output signalif the O.K.'key-is depressed causing the closure of the corresponding ok contact, since BSS is in its 1 condition. However, -this will only be a transient signal which will only last some 30 microseconds. It will be assumed that .such a transient signal cannot be elective to register a correct proof which would cause the carriage to be positioned to the right to permit the keying of the amount of the cheque. Hence, the operator has no opportunity to skip a correct proof. The 30 microseconds duration mentioned above is due to the fact that 30 microseconds after the trailing edge of the Pb pulse occurred, the moment at which tube 0 of CTI became conductive, a Pc pip will occur. This will pass through G6, trigger BSZ back to the 0 condition whereby a corresponding trigger pulse appears at terminal P7, which pulse can go through gate GI and reach terminal PIZ to trigger BSS back to its 0 condition. Hence, from that moment it is already impossible to obtain an O.K. signal. l

The bistable circuit BSS having been returned to its 0 condition, the next Pb pulse which during the first operation-would have been able to go through G10 since BSZ is in its 0 condition, is blocked as a result of BSS being in its 0 condition. Hence, from the moment that v CTI has arrived in its 0 condition, the counters will be driven byl the same Pb pulses, i.e. those alternate pulses ilowing through G8. This is the second operation, i.e. the counters CTI and CTZ exchange their conditions. Since `CTZ was in the 9 condition when C'TI was in the 0 condition, after two Pb kpulses have driven the'counters, CTZ will arrive in its 0 condition while CTI will be placed in its 9 condition.

' The Pc pip which follows will trigger BSZ toits 0 condition and the trigger pulse generated at terminal P7 will this time pass through GZ to reach terminal P13. Since BSS is in the 0 condition, a trigger pulse delayed by 15 microseconds by the action of MSI willarrive at the 0 input of BSI, through the mixer GII, placing the bistable circuit in the 0 condition. As described for the rst digit, thel result of this will be to empty the .counter /CTZ after `stopping both counters.

The third digit, i.e. 4, can now be keyed with CTI in its 9 condition. The first voperation will be essentially similar to that described for the keying of the .second digit and after counter CTI has been driven by 9 Pb pulses, counter CTZ will have been `driven by 18 Pb pulses. Hence, since counters CTI and CTZ were originally in their 9 and 4 conditions respectively, theyv are now -both in their 0 condition. Accordingly, the trigger pulse which appears at terminal P7 as a result of the next 'Pc pip triggering BSZ to its 0 condition, will be able to pass both through gate G1 and through gate GZ. Simultaneous trigger pulses will therefore appear at iteryminals PIZ and P13.

It will be remarked thatduring the advancement of the two counters, counter CTZ already reached its 0 condition while counter CTI had only reached its 6 condition. Hence, a trigger pulse coinciding with a -Pc pip appeared at the output of GZ to which terminal P13 isA connected. This trigger pulse a-t terminal P13 will trigger the monostable circuit MSI but .the pulse generated at the output of MSI when this circuit returns to its stable condition after. l5 microseconds will however be without effect since gate G14 is blocked by virtue of BSS being in itsl condition. Y

Returning now to the case of simultaneous pulses' appearing at terminals P12 and P13, the pulse at terminal v P12 will reach the 0 input of BSS through the mixer GIZ --Here, theY usefulness of the monostable circuit MS1 producing a delayA of some 15 microseconds can be appreciated, since without this delay, BSS would be triggered by the pulse at terminal P12 while simultaneously the pulse at terminal P13 would be applied to the gate G14. Hence, the passage of the pulse at terminal P13 through the gate G14 would not be ensured, or at any rate, one would not be sure of obtaining a pulse of suitable shape atthe output of gate G14.

It should be observed that the essential thing is to avoid coincidence of the two pulses which may arise simultaneously at terminals P12 and P13 when both' the counter CT1 and the counter CTZ are in their 0 positions.` Accordingly, it would be possible to insert the monostable circuit MS1 between terminal P12 and the mixer G12, while terminal P13 would be directly connected to the gate G14. In this case however, the pulse at terminal P13 and directly connected to gate G14 would not be able to go through that gate since BSS would still be in its l condition. After 15 microseconds, BS3 would be triggered into its condition by the pulse at terminal P12, but at that moment, the pulse at terminal P13 would already have disappeared. In such a case BSl would not be triggered to its 0 condition and Pb pulses would con tinue to tlow through gate G7 and through gate G8 for every alternate Pb pulse corresponding to BSZ being in its 1 condition. Hence, a -full cycle for both counters with Pb pulses applied simultaneously to both counters would be made until both counters would again reach their 0 conditions at the same time. Then, the pulse at terminal P13 would be able to go through the gate G14 and the mixer G11 to trigger BSl to its 0 condition, thereby stopping the second operation resulting from the keying of the last digit.

As `shown above, this second operation will not takeY place in the case of the last digit, since both Vcounters having reached their O conditions simultaneously, there is no point in per-forming the second operation which is merely an exchange of the conditions of the two counters. There would be a point for making this second operation even in the case of the last digit and for the sake of uniformity, if extra equipment was necessary to cover the case of the last digit. However, no extra equipment is needed and it may bedeemed preferable to avoid this secondoperation in that case since there is a slight gain of time of two Pb pulse periods, considering the maximum time to be reckoned for the operations following the de- Y pression of any digit key for any initial position of counter CTI..

When BSI is returned to its 0 condition after the two counters CTI and CTZ have reached their 0 conditions, a further pulse will be applied to CTZ in the manner previously described so as to empty that counter. Also,

YB83 will be returned to its l condition.

Since a number satisfying the specified condition has now been keyed, it is possible for the operator to depress the O.K. key and obtain a signal from the output gate G3 which will reach the Ok terminal through the 0k contact corresponding to the key. I-n a manner not shown, the effect of this signal at this terminal will be to cause the printing of the account number which has been keyed and also to cause the dispiacement of the carriage tothe right-hand position in which the amount mentioned on the cheque can now be keyed.

The carriage having been moved to the right-hand position, contact Ik is opened and relay Lr releases. In turn, relay Lm' releases due to the opening of contact [r1 and finally relay Lbr releases following the opening of contact larl. As contact [r3 opens before the closure of contact lbrl, relay Cr has no opportunity to reenergise. Also, since contact [r2 is reclosed before the reopening of Contact larg there is no opening of the connection between v terminal P6 and the l input of the bistable circuit BSO,

interruption which might otherwise interfere with the operation of relay Lr.

its contact rr2 opens the normally closed connection between terminal P6 and the O input of BSI). In a manner previously described, this opening will now place BSO in its 0 condition. The operation of relay Rr produces the energisation of relay Rar by means of make contact rrl and the closure of contact mrl re-establishes the circuit between terminal P6 and the 0 input of B80.

Since the bistable circuit BSO is now in its O condition, the depression of the digit keys and the release thereof when keying the amount, although this will be effective in triggering the monostable circuit MS() in a manner previously explained, will not be eiective to start the proof operations since gate G5 will remain blocked. Since CT1 remains in its 0 condition during the keying of the amount and since BSS remains in its 1 condition, a signal will remain at the output of the gate G3 where- Vby the same O.K.v key can be used by the operator after having keyed the amount, in order to obtain a signal at the Ok terminal which will shift the carriage. Means not shown will of course be provided so that a signal at the Ok terminal shifts the carriage to the left-hand position when it is originally in the right-hand position and 4vice-versa. Hence, the circuits are so arranged that the same OK signal either gives permission to the operator to key the amount when the account number has been correctly keyed or gives permission to the operator to key the next account number when the previous amount has been keyed.

The return of the carriage to the left-hand position will again close the contact lk with the results already given while the reopening of Contact rk will cause the release of relay Rr followed by the release of relay Rar, this sequence preventing any further interruption of the connection between terminal P6 and the 0 input of BSO.

If a single wrong `digit has been'keyed or if a single transposition of any two diiferent digits has been made, an error will certainly be detected, i.e. the faulty number will not be one of those satisfying the specified relation. In such a case, when the O.K. key is depressed, counter CTl will not be in the 0 condition and an OK signal will not be obtained. The absence of this signal after the depression ofthe O.K. key can readily be used by means not shown to cause some kind of signal such as an optical one to be provided to the operator to indicate a fault. As the carriage has not moved following the depression of the O.K. key, this signal will indicate to the operator that a cancellation of the account number which has just been keyed but which has not yet been printed, should be performed.

The operation of the cancel key (not shown) will resultin the closure of the contact ck, closure which will establish a circuit between terminals P0 and P3 to energise relay Cr. The operations following theenergisation of relay Cr are exactly those which were described previously when this relay was operated as a result V0f ythe The cancel key willof course be depressed only momentarily and may be of the push button type. Care should however be taken that contact ck is closed for a time sufficient to permit the energisation of relay Cr so that the remaining relays, i.e. Car, Cbr, Ccr and vCdr can all be operated momentarily. The operation of 'the cancel key will thus permit to wipe out the counters CT1 and-GT2 and reset all the circuits in readiness for rekeying the account number.

The time of the operations following the depression of a digit key is essentially determined by the sum of the times required for shifting the CTZ counter to its 0 condition while CTI yis shifted at twice the rate, plus the time required for the second operation consisting in shifting the counter CTZ until it reaches its 0 condition, counter 'CT1 being simultaneously shifted at the same rate. When a digit other than the iirst or the second is keyed, counter CT1 might initially stand in its 10 condition and accordingly 20 Pb pulses might be necessary to drive to its condition, since only half of these 20 Pb pulses will be effective for advancing counter CTI. Moreover, although when CTI is in its 0 condition when the first digit is keyed and that dueto BSS being in its 0 condition, the rst operation is not performed, it may happen that CTI is in its 0 condition when some other digit is keyed. In that case, since BS3 is now in its 1 condition, 22 Pb pulses will be necessary to make a complete cycle for CT1 and two complete cycles for CTZ. Hence for the maximum time of the lirst operation one should reckon with 22 Pb pulses.

In turn, counter CTZ might have to be stepped from its 10 condition to its 0 condition by means of another set of 20 Pb pulses since only half of these are applied both to counter CT1 and to counter CTZ. Altogether, one must thus reckon with a maximum time corresponding to 42 Pb pulses. An electronic counter of the pattern shift register type disclosed in the U.S. patent to Odell, No. 2,649,502, issued August 18, 1953, can readily work with stepping pulses at a period of 200 microseconds. Hence, 42 Pb pulses correspond only to 8.4 milliseconds which, even with very fast operators and with no slowing of the key operation, is sufficiently smaller than the time required by the operator to key one digit. However, if one should desire to use a pattern shift register of a type which cannot work at such relatively fast rate, the time interval corresponding to the 42 Pb pulses will become correspondingly larger and the difference between this time interval and the time interval between the keying of two digits might become too critical. In such border line cases, it might be of advantalge to limit the operation time to something less than 42 Pb pulses, or in general to something less than 2 (2p-1,) Pb pulses if p is a modulus other than 11. An obvious way to have a maximum time less vthan 42 Pb pulses would be to make every Pb pulse effective when CTZ is driven to its 0 condition while CT1 is driven at exactly the same rate. There is no fundamental reason why this should not be performed, and in fact the only reason why every alternate Pb pulse only is used for driving both counters when CTZ is being driven to its 0 condition, is one of circuit design. As shown in Fig. 2, by applying stepping pulses to both counters only when BSZ is in its 1 condition, one ensures that immediately after counter CTZ having reached its 0 condition, BSZ always returns towards the 0 condition which is the reset condition and in so doing generates a pulse at terminal P7 which will stop the ilow of further stepping Pb pulses.

By modifying the circuit design, one could however reduce the maximum time of 22|20 Pb pulses to 22`l10 Pb f pulses.

A second embodiment of the invention will however be described as permitting the reduction of the maximum time to 20 Pb pulses.

Referring to Fig. 5, the latter shows an arrangement wherein each of the two counters alternatively serves to register the incidentV digit instead of using a particularl predetermined counter such as CTZ in Fig. 1 for that purpose. Fig. shows a rst counter unit` CTU, which has been representedin detail, while the second counter unit CTU hasbeen shown as a block schematic sinceit is identical to the counter unit CTU. Each counter unit has eight outside terminals such as P17 to P24 for CTU and the corresponding terminals for CTU are labelled from P"17 to P'Z4.

The control and start circuit CSC' used in conjunction with the counter units CTU and CTU is essentially similar to the circuit CSC detailed in Fig. 2 except for a few changes which have been shown in detail in Fig. 6.

The essential principle of the operation -for the embodiment shown in Fig. 5 is to store the incident digit on one counter and merely to step the other counter to its 0' condition while the counter which hasV received the Y first operation which was performed with the arrangement of Fig. 1, but with that of Fig. 5 no further stepping takes place after this; the counter which has been stepped to its 0 condition is merely wiped out and the next digit is stored in that counter, this being followed by a stepping operation similar to the one just described. In other words, the two counters continuously interchange their functions. ln order to define this exchange of functions as each digit is keyed, an additional bistable circuit BS4 has been used for the scheme of Fig. 5, this bistable circuit operating as a scale-of-two-counter with? a common input in the same way as BSZ in Fig. 2.

The initial resetting operations when the carriage is in the left-hand position in readiness for the keying of an account number, are exactly similar to those previously described but by referring to Fig. 6 showing some moditi cations tothe circuit of Fig. 2, it will be seen that when contact ccrz is opened'to reset' the bistable circuit, such as BSI, to its 0 condition, the potential at terminall Pf6' will no longer be applied to terminal P15 and the bistable circuit BS4 (Fig. 5) will also be set into its 0 condition.

The circuits having been properly reset, one can now describe the operations subsequent to thev keying of theV account number such as 254 previous used in conjunction with the circuit of Fig. 1. The fact that the scale-of-A two-circuit BS4 is always reset to a predetermined condition before an accountnumber is keyed, is used to always key the first digit of an account number in counter CTZ of the first unit CTU. Since BS4 is in its O condition,

a suitable potential is present at terminal P23 whichv will be impressed on the starter elect-rode of tube 2 in counter CTZ when the key corresponding to the digit 2 is der pressed, causing the temporary closure of contact km. It'

should be mentioned that the key contacts such as kzi are duplicated in the unit CTU sothat a contact corre?-` sponding to k21 will be closed thereby connectingtermi.-l nal P'Z3 to tube 2 of counter CT1. Since BS4 4is in its. 0 condition there is however no suitable potential aty thisl terminal which could cause tube 2 in CTI to become conductive. It should also be mentioned that the positionsy or stages of counter CTI which has'` not been shown in Fig. 5, lare numbered in exactlyv the same way asy the. positions were numbered for counter CTI shown in Fig.` l, i.e. the second position fromJ thevrightf corresponds to 1, the third position from the right corresponds to 2, etc., whereas the oppositenumbering is used` for counter This means, of course, that there is adistinctionbetween'i the connections of the key contacts to the two units since' the contact such as -k2-1 is` connected to the second stage' of counter CTZ starting from; the left, while the corre.-v sponding key contact is connectedj tol the third' stage of counter CT1 starting from the right. Also, at the end: of the resetting operations, when contact cdr2. closes,the potential at terminal P`23'will be applied to terminal P19^ and from there to.y terminal PIS which, as shown by the connection of terminal P18 lin' unit CTU'is connected to the 0 stage of lcounter CTI (not shown) in unitCTU.V On IJthe other hand, the connection between terminals- P'I'9 and PI'S shouldnotv be made since the ionization:v of the 0 tube is only required' initially for the counter, i.e.- CT1, which does not receive the rstY digit of the account number. Hence, contact cdrzneed not bedupli-Y cated in order to vinterconnect terminals Pf19andfP-I8`-l which have only been shown in order to permit the description; of the circuits by showing the detailed arrangement ofunit CTU only. l

As already explained, the release of the key corre-- sponding to digit- 2 will result in at leastV one Pa/v pulse being ableto pass through gate G5 and thereby to trigger BSIl into its 1 condition. Referring toFg. 6,71 gate GT has been modified with respect toy gate G7 shown' inf Fig. 2. An additional inhibiting input shown byfarblack arrow and indicated by the numeral -1 inside thecircle`` representing' the gate, has been used. This inhibiting input is connected to terminal P12 which constitutes the output of `a mixer G16 whose two inputs are connected to terminals P17 of unit CTU and to terminal PI7v of unit CTU. Initially, counter CTI (not shown) is in its condition and accordingly, the gate corresponding to G17 delivers an output signal, this being due to BS4 being in its O condition, whereby terminal P24 receives a suitable potential partly responsible for delivering an output at terminal PI7. On the other hand, an output cannot be present at terminal P17 since G17 is blocked by virtueof BS4 being in its 0 condition. The output signal initially present at terminal P12 is used to block gate G7 with the result that the counters are not advanced.

However, the rst Pc pip following the Pa pip which put BSI in its 1 condition will trigger BSZ into its 1 condition. The unblocking of gate G8 will be without effect since G7 is blocked. The second Pc pip will return BSZ into its 0 condition and in so doing a pulse will be generated at the output of BSZ which, instead of being applied to terminal P7 as in Fig. 2, will be applied to a gate G15 which is controlled also by the potential present at terminal P12. This trigger pulse will pass gate G15 and through the mixer G11 will `arrive at the 0 input of BSI thereby triggering BSI back to its 0 condition.

As before, a consequence of the return of BSI to its 0 condition will be that a pulse is generated to trigger MS2 from its stable to its unstable condition. At the Sametime however, the trigger pulse at the output of BSI will be applied to terminal P16 which Fig. 5 shows to be connected to the common input of BS4. Hence, at the same time that MS2 is triggered, BS4 moves into its 1 condition. This means that the gate in CTU' corresponding to G17 in CTU is blocked since the potential at terminal P'24 has disappeared and accordingly the output potential at terminal P12 also disappears whereby G7 is no longer blocked. However, since BS4 can only be triggered as a consequence of BSI having first been triggered, no further Pb pulses are allowed through gate G7. When MS2 returns to its stable condition after 30 microseconds, an output trigger pulse is generated, as before, to trigger MSS as well as to place BS3' into its l G7. When MS2 returns to its stable condition after 30 microseconds which is applied to terminal P9 through the mixer G9. In Fig. 5, terminal P9 is connected to terminal P22 of unit CIU and to the corresponding terminal P'22 of CTU'. In unit CTU, terminal P22 is connected to one input of the gate G18 whose other input is connected to terminal P23. A similar gate of course exists 1n unit CTU with its second input connected to terminal P24. Since BS4 has been triggered into its 1 condition, 30 microseconds before the appearance of the 30 microsecond pulse at terminal P9, gate G18 is blocked and the wipmg out pulse will not be effective in unit CTU since it cannot reach the commoned cathodes through the mixer G19. In unit CTU however, the gate corresponding to G18 is unblocked and the wiping out pulse will pass through the mixer corresponding to G19 to advance the information on counter CTI by one step. Since CTI is in its 0 condition, the 0 tube will be extinguished. As BSI has already been returned to its 0 condition, there is no potential at terminal P8, which is connected to terminals P20 and P20, to unblock the gates such as G4 in CTU. Hence, tube 0 of counter CTI will be extinguished and no other tubes will be lit as required, in readiness for the keying of the second digit which will now be stored in counter CTI.

It will be appreciated that the inhibiting control exerted on gate G7 is of some use since if the arrangement of Fig. 2 has been retained, the information in counter CTI as well as the information in counter CT2 would have been stepped by every even Pb pulse until tube O in counter CTI would again be lit, whereafter the trigger pulse ygenerated at the output of BSZ when this. circuit iSV returned to its 0 condition would have stopped the operations by passing through gate GIS and the mixer GII to reach the 0 input of BSI.' In fact the advantage is small since using the previous arrangement would cause the maximum time of operation to Vcorrespond to 22 Pb pulses,

whereby the present arrangement of Figs. 5 and 6 will permit the limitation of the time of operations to 20 Pb pulses.

The circuits are now ready for the keying of the next digit i.e. 5. Since BS4 is now in its l condition, tube 5 in counter CT2 cannot be ionized due tothe depression of the key but tube 5 in counter CTI will be made conductive. Since it is only tube 2 which is lit in CT2, gate G17 cannot deliver an output reaching terminal P12 through the mixer G16, and as the gate corresponding `to G17 is also unable to deliver an output to terminal P112 due -to BS4 being in its l condition, gate G7 is no longer initially blocked. Therefore, as soon as BSI has been triggered into its l condition following the release of the key corresponding to digit 5, a rst Pb pulse will be able to flow through gate G7. This pulse will also pass through gate GI0 which incidentally is no longer controlled by the l condition of -the bistable circuit BSS. This was useful in the case of the circuit of Fig. l in order to start immediately with the transfer operation, i.e. exchange of the counters positions, and this for the rst digit of the account number. In the present case however no such transfer takes place. The iirst Pb pulse at the output of G10 rwill reach terminal P9 through the mixer G9 and will therefore be applied to terminals P22 and P22. Since BS4 is in its l condition, this first Pb pulse -will only pass through the gate in CTU which corresponds to gate G18 and only counter CTI will be driven from its condition 5 to its condition 4, CT2 remaining in its 2 condition.

The second Pb pulse will be able to pass through G8 and reach terminal P10 which is connected `to terminals P21 and PZI. Hence, this pulse will step both counters after passing through the mixer such as G19 for the counter CT2. This process will continue, i.e. the odd Pb pulses driving CTI and the even Pb pulses driving both CTI and CT2, until CT2 reaches its O condition. At that time, CTI has reached its 9 condition. Counter CTI Went through its 0 condition during the stepping operation, since 18 Pb pulses were needed but the gate GI7 could not however deliver an output since BS4 is in its l condition. On the other hand, when CT2 reaches its O` condition, gate G17 delivers an output which results in the stepping operation being stopped due to the return of BSI to the 0 condition, an additional pulse being fed by MSS to counter CT2 in the manner previously explained.

The circuits are now ready for the keying of the last digit, i.e. 4, BS4 being again in its 0 condition. Accordingly, Itube 4 of CT2 will be ionized, tube 9 in CTI still being ionized as well. The Pb pulses will be applied to the counters CTI and CT2 in exactly the same manner as previously explained for the keying of the first digit. 9 Pb pulses will be applied to CTI during the time that 18 Pb pulses are applied to CT2. Hence, both counters will reach their respective 0 conditions simultaneously after the 18th Pb pulse and immediately thereafter, the next Pc pip will trigger BSZ back to its O condition. Since gate GI7 delivers an output signal at terminal PI7, the trigger pulse at the output of BSZ will pass through G15 in the manner already explained and the operations will be stopped, the 0 tube in CTI being deionized. Since the bistable circuit BS4 has now been placed in its 1 condition, the fact that CT2 is in its O condition will produce an output signal at terminal P17 which is applied to gate G20 through the mixer G16. Since BSS is now in its 1 condition, an output signal is present at the output of G20. When the operator depresses her O..K key, the closure of contact ok Will apply a potential at terminal Ok which willvindicate that the account number has been correctly keyedl and cause thecarriage to be moved to the rightin preparation for the keying of the correspondingamount of the cheque.

For the embodiment which has just been described, the maximum time for' Athe keying of one digit corresponds to 20 Pb pulses only or more generally to 2(p-l) pulses, p being the modulus. Thus the maximum time of operation to be reckoned with has been halved with respect to the maximum time required for the embodiment of Fig. l.

By a modification of the circuit of Fig. 5, it is possible to still reduce this maximum of operation corresponding to the keying of one digit and a maximum time corresponding to 10 Pb pulses or more generally p-l pulses can be obtained.

The modification to the circuit of Fig. 5 is shown in Fig. 7. This figure represents only those parts of Fig. 5 which need be modified the remaining parts being identical to those shown on that previous iigure. Referring to Fig. 7, anl additional coincidence gate B21 has been inserted between stage 5 and stage 6 of counter CTZ. This additional gate G21 is controlled in a way similar to the control of gate G4 linking stage 0 with stage l, by the potential appearing at terminal P20 and derived from terminal P8 of unit CSC' of Fig. 6. Also, just as the output of stage is applied to a gate G17, the output of stage is also applied to a further gate `G22 also controlled by the potential at terminal P24. The output of this gate G22 is connected to a terminal P25 leading to a mixer G23. The modifications shown-for counter CTZ should also be made for CT 1 and accordingly, the mixer G23 also receives an input from a terminal PZS (not shown) which inV unit CTU^ corresponds to terminal P25 in unit CTU.

The output of the additional mixer G23 is connected to a further terminal PlZin the control circuit CSC (Fig. 8) which should be slightly modified with respect to CSC shown in Fig. 6 and which already showed a modification of the original control circuit CSC shown in Fig. 2. Just as. terminal P12 constitutes the input of the gate G15 whose other input is connected so as to receive the trigger pulses generated when BSZ returns to the O condition, terminal P'12 constitutes one input of a further gate G.' 15 whose other input is constituted by exactly the same pulses. The outputs of the gates G15 and G15 are both connected to the mixer Gll but in addition, the output of gate G15 is connected to the 0 input of a further bistable device BSS, while the output from G15 is connected to the 1 input of this bistable device. Further, the signal at terminal P12 again exerts an inhibiting action on the gate G"7 and the same applies for the signal at terminal P12. Whenever a signal is present at terminal P12 or at terminal P'1Z, the gate G7 will therefore be blocked. Finally, the pulse which is produced by the monostable circuit MS3 can passv through the gate G24 when BSS is in its 1 condition to the mixer G25 whose other input is constituted by the output of gate G8, and whose output is connected to terminal P10.

The elect of the changes which have just been described is the following. When CTZk has to be advanced to its 0 condition, but if it is at least six stepsV away from this condition, i.e. in conditions l, 2, 3, 4 or 5, condition 5 will act as the detecting condition instead of the 0 condition. Since to the six pulses needed to advance CTZ from its 5 condition to its O. condition correspond twelve advancing pulses for the other counter CT1, this counter will not be advanced by the right number of Pb pulses, i.e. twice the number used to drive CTZ. ,However, since the least non-negative residues with respectto l1 are the quantities which matter, CT1 can still reach the right condition by being fed with one additional Pb pulse after CTZ has reached 'its S condition. When this is the case, and assuming of course that BS4 is in its 1 condition, the

potential at terminal P24 Vin conjunction with the fact thatV tubeV 5 of CTZ. is` ionized, will cause a signal tol appear at terminal P25 and to reach terminal P12 through the mixer G23. The immediately following Pc pulse will cause a trigger pulse to be generated by BSZ when returning to its O condition and this trigger pulser will be able to pass through gate G15 (Fig. 8). From the output of G15, this pulse will pass through the mixer G1-1 and stop the advancement of the two counters in the manner previously described. This trigger pulse will also place BSS in its l condition or leave it ink that state if it was originally in the l condition. Hence, when MSS delivers an output pulse of microseconds, this will be applied not only to terminal P9 through the mixer G9 in order to deioni'ze tube 5 in CTZ, but also to terminal P10 through the gate G24 and the mixer G25. Hence, counter CT1 in unit CTU will receive an additional Pb pulse asy required and will thus reach the correct condition. Since G21 is controlledby the potentid at terminal P20, which is connected to terminal PS, since there is also no potential at terminal P24, which performs an additional control on G21', BS4 havingbeen returned to its 0 condition, the de-ionization of tube 5 in CTZ will not produce the ionization of tube 6 and the counter CTZ will thus be ready for the keying of the next digit. The additional control on gate G21 by the potential at P24 will however permit counter CT1 to reach its position 5 due to the extra pulse, if it stood in position 6 when the normal advancement was stopped. In unit CTU (not shown) the gate corresponding to G21 is, of course, located between stage6 of counter CT1 and stage 5, since for that counter the stages are numbered in reverseorder with respect. to thestages of counter CTZ', i.e. the same num'- bering as in Fig. 1. Hence, for counter CT1, despite the absence of a potential at terminal PZ since BSI is now back in its O condition, thepotential at terminal P'24 due to BS4 having been placed in its O condition will allow tube. 5to be ionized in counter CT1 if the pulse generated by MS3 causes the de-ionization of tube 6 in CT1. On the other hand, if counter CT1 has to pass from its 6 condition to its 5 condition while the Pb pulses are being applied, despite the fact that there will be no potential at P24 since BS4 is. in its l condition, the fact that BSI is in its l condition permits the gate corresponding to G21 to be conductive.

The arrangement of Fig. 7 could of course bev applied to the arrangement of- Fig. l, but when it is applied to the arrangement of Fig. 5, one obtains the smallest maxiA mum number of Pb pulses or more generally p-l.

It will be observed that the method of sending Pb pulses to one counter and half the number of Pb. pulses to the other counter bymeans of the bistable circuit BSZ, has the advantage that the counters are driven by identical pulses both as to their period and as to their duration. Y Hence, if there exists some kind of optimum duration for driving the counters in the most satisfactory way, this optimum duration is always used. Also, BSZ is always returned to its original condition whatever number of Pb pulses is applied to the counters, and this means that after the keying of any digit, the arrangement is ready to be used again without the eventual reset of BSZ.

It is evident that the arrangements described can also be used to calculate the so-called proof digit after any normal number has been keyed. This can be done for all three embodiments in` av manner similar to that described in the Linsman application, Serial No. 484,715, abovev mentioned.

It is also clear that the number of stages of the counters need not necessarily be equal to the number of distinct conditions. Four-stage binary lcounters using feedback connections to obtain cycles of 1l conditions could, for example, beused.

Finally, while the embodiments described have used values of p=l1 and of r=2 and s=1 (Fig. 1), r=s=2 (Figs, 5 and 7), the invention is obviously not limited to these particular values as will be clear from the beginning of the description.

While the principles of the invention have been described above in connection with specific apparatus, it is to be clearly understood that this description is made only by Way of example and not as a limitation on the scope of the invention.

What is claimed is:

1. Calculating equipment, for calculating a digital function which can take any value out of p different values from zero to p-l, Where p is a predetermined integer, comprising a first counter and a second counter, each counter having at least p stable and distinct conditions and adapted to be stepped cyclically from one condition to the next, p steps causing the return of the counter to its initial condition, means for setting said counters in their initial conditions, means for causing said first counter to step at one rate while simultaneously causing said second counter to step at a multiple of the stepping rate of said first counter, means for simultaneously stopping the stepping action of both counters when said first counter reaches a predetermined condition, means responsive to said first counter reaching said predetermined condition for causing said second counter to step at one rate and simultaneously causing said rst counter to step at a multiple of said one rate, and means for simultaneously stopping the stepping action of both counters when said second counter reaches a predetermined condition.

2. Calculating equipment, as defined in claim l, in which the means for causing the counters to step at different rates comprises an auxiliary counter and means for controlling the stepping of the counters dependent upon the condition of said auxiliary counter.

3. Calculating equipment for calculating a digital function which can take any Value out of p different digital values from zero to p l, where p is a predetermined integer, comprising a first counter and a second counter, each of said counters having at least p stable and distinct counting conditions and each adapted to be stepped cyclically from one condition to the next, p steps causing the return of the counter to its initial condition, means for setting said first counter in an initial condition, means for setting said second counter in an initial condition, means for causing said first counter to step at one rate while simultaneously causing said second counter to step at r times said rate, r being an integer greater than 1, means responsive to said first counter reaching a predetermined condition for simultaneously stopping the stepping action of both counters, means controlled by said first counter in its first predetermined condition for thereupon causing said second counter to step at one rate while simultaneously causing said first counter to step at s times said rate, s being an integer greater than l, and means responsive to said second counter reaching a predetermined condition Ifor simultaneously stopping the stepping action for both counters, whereby the condition finally attained by said first counter is a digital function of the initial conditions of said first and said second counters defined by where x1 is the number of steps required to bring said first counter from its initial condition to its first predetermined condition, y, is the number of steps required to bring said second counter from its initial condition to its first predetermined condition, and x,-+1 is the number of steps required to bring said first counter from the condition finally attained to its predetermined condition.

4. Calculating equipment for calculating a digital function which can take any value out of p different digital values from zero to p-l, where p is a predetermined integer, comprising a first counter and a second counter, each having at least p stable and distinct conditions and adapted to be stepped cyclically from one condition to the neXt, p steps causing the return of the counter to its initial condition, a bi-stable device, means controlled by said bi-stable device being in a first condition for applying signals to said second counter to cause it to assume an initial condition, means controlled by said bi-stable device for applying` signals to said counters for causing said first counter to step at one rate while simultaneously causing said second counter to step at r times said rate, r being an integer greater than 1, means responsive to said rst counter reaching a first predetermined condition for simultaneously stopping the stepping action of both counters, means responsive to said stopping means for causing said bi-stable device to assume its second condition, means controlled by said bi-stable device being in its second condition for applying signals to said first counter only to cause said first counter to step to another condition, means responsive to said first counter being in said other condition for operating said bi-stable device to cause signals to be applied to vsaid counters for causing said second counter to step at one rate While simultaneously causing said firstcounter to step at s times said rate, s being an integer greater than 1, means responsive to said second counter reaching a predetermined condition for simultaneously stopping the stepping action of both counters and for causing said bi-stable device to assume its first condition, whereby after each stepping action, the condition attained by the counter stepped at r or s times the rate at which the other counter is simultaneously stepped is the digital function of the initial conditions of both counters before said stepping action defined by Y21'E(Y2t 2x2t1) mod- P x2i+1E(x2i-5y2i) mOd- Pl where x2i 1 is the number of steps required to bring the first counter from its initial condition to its predetermined condition, y2, 1 is the number of steps required to bring said second counter from its initial condition to its predetermined condition, y2, is the number of steps required to bring said second counter to another condition from the condition attained afterhaving been stepped r times the rate of said first counter, xzi is the number of steps required to bring said first counter from its other condition to its predetermined condition, and x2i+1 is the number of steps required to bring the first counter to its predetermined condition from the condition attained after having been stepped at s times the rate of said second counter.

5. Calculating equipment, as defined in claim 3, Wherein p is odd and either r or s is equal to 2 mod. p or both r and s are equal to 2 mod. p, further comprising means for stopping a counter'which is being stepped at half the rate at which the other counter is being stepped when it reaches a third predetermined condition, and means for stopping the other counter after it has taken one additional step,

steps being required to bring the first mentioned counter from its third predetermined condition to its first or second predetermined condition.

6. Calculating equipment, as defined in claim 5, in which the means for causing the counters to step comprises a scale-of-2 counter, means for normally maintaining said scale-of-Z counter in a first condition, means responsive to said scale-of-Z counter being in said first condition for causing a signal to be applied to the second counter to cause it alone to step, means responsive to said scale-of-Z counter being in its second condition for causing a signal to be applied to both said counters to cause them both to step, and means for changing the condition of said scale-of-Z counter each time said second counter steps, whereby when the stepping is stopped upon said irst counter reaching its predetermined condition, said scale-of-Z counter is always back to its rst condition.

7. Calculating equipment, as dened in claim 3, in which the means for causing the counters to step comprises a scale-of-Z counter, means for normally maintaining said sca1eof2 counter in a rst condition, means responsive to said scale-of-Z counter being in said first condition for causing a signal to be applied to the second counter to cause it alone to step, means responsive to said scale-of-Z counter being in its second condition for causing a signal to be applied to both said counters to cause them both to step, and means for changing the condition of said scale-of-2I counter each time said second counter steps, whereby when the stepping is stopped upon said rst counter reaching its predetermined condition, said scaleof2 counter is always back to its rst condition.

References Cited in the le of patent UNITED STATES PATENTS 2,634,052 Block Apr. 7,1953 10 2,684,199 siarreveld i July 2o, 1954 2,684,201 Starreveld July 20, 1954 FOREIGN PATENTS Y 709,407 Great Bn'tain May 26, 1954 

